Spectral Analysis of Large Dimensional Random Matrices
The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random va
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Spectral Analysis of Large
ond tion
Springer Series in Statistics
Zhidong Bai Jack W. Silverstein
Spectral Analysis of Large Dimensional Random Matrices Second Edition
Springer Series in Statistics Advisors: P. Bickel, P. Diggle, S. Fienberg, U. Gather, I. Olkin, S. Zeger
For other titles published in this series, go to http://www.springer.com/series/692
Zhidong Bai Jack W. Silverstein
Spectral Analysis of Large Dimensional Random Matrices Second Edition
Zhidong Bai School of Mathematics and Statistics KLAS MOE Northeast Normal University 5268 Renmin Street Changchun, Jilin 130024 China [email protected] & Department of Statistics and Applied Probability National University of Singapore 6 Science Drive 2 Singapore 117546 Singapore [email protected]
Jack W. Silverstein Department of Mathematics Box 8205 North Carolina State University Raleigh, NC 27695-8205 [email protected]
ISSN 0172-7397 ISBN 978-1-4419-0660-1 e-ISBN 978-1-4419-0661-8 DOI 10.1007/978-1-4419-0661-8 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009942423 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
This book is dedicated to:
Professor Calyampudi Radhakrishna Rao’s 90th Birthday Professor Ulf Grenander’s 87th Birthday Professor Yongquan Yin’s 80th Birthday
and to
My wife, Xicun Dan, my sons Li and Steve Gang, and grandsons Yongji, and Yonglin — Zhidong Bai My children, Hila and Idan — Jack W. Silverstein
Preface to the Second Edition
The ongoing developments being made in large dimensional data analysis continue to generate great interest in random matrix theory in both theoretical investigations and applications in many disciplines. This has doubtlessly contributed to the significant demand for this monograph, resulting in its first printing being sold out. The authors have received many requests to publish a second edition of the book. Since the publication of the first edition in 2006, many new results have been reported in the literature. However, due to limitations in space, we cannot include all new achievements in the second edition. In accordance with the needs of statistics and signal processing, we have added a new chapter on the limiting behavior of eigenvectors of la
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